Will it be a foul?

What do you mean springboard?
You step on ur partner back to jump higher?
If yes then forget ur imagination.

Fault or not, its very useless & dangerous.
Double games are fast pace games, how long the times you & ur partner get ready for the jump?
If you execute to fast, there is a risk ur feet slipped or ur friend out of balance, & not to mention if you manage to jump high, you risk urself falling from the extra height. This are very risky for both of you. Its badminton not circus attraction.

Let say the crazy, you manage to execute it perfectly. When the opponent are able to return ur very step smash, how would ur side response? Ur springboard partner are unbalance due to ur kicking his back. U urself havent landing coz you jump very high, or let say you manage to land, there is a huge downforce that would delay ur next movement. So basically losing score.

Realistically, badminton games are 21 point / 2-3 match. Simply 42 point for you to win if you manage to score everytimes. How many times you could do springboard jump perfectly without injury? On high level, how many times you could get easy shot to execute the plan? The risk are just not worth it & even the standard badminton are already risky itself, dont need to add more risk for less to no gain.

Improve ur basic technique rather than freestyle badminton parkour stuff.